In a large saucepan, combine the konbu and water and heat over medium-low heat almost to the boiling point. Remove the konbu just before the mixture comes to a boil and discard. Add the bonito flakes and allow to steep for 10 seconds, or just until the mixture comes to a boil.

Turn off the heat and skim any foam that has come to the surface of the liquid. Allow the mixture to stand for 2 minutes, then strain through a fine mesh sieve or cheesecloth. Discard bonito flakes and return the dashi to the saucepan over low heat. Add the reserved lobster body and shells to the dashi and allow to steep for 5 minutes. Remove and discard shells and body.

Quickly rinse or wipe off the mushrooms to remove any loose sand or dirt, then add the mushrooms to the dashi and allow to steep over low heat until the mushrooms are softened, about 10 minutes. Remove the mushrooms and, when cool enough to handle, slice them crosswise into thin slivers, and return them to the dashi. Add the lobster meat and continue to cook until heated through, about 2 to 3 minutes. Stir in the soy sauce, white and brown misos, and scallions and combine well. Serve immediately.